C~1 Smooth Triangular Surface Patch Constructed by C-curves

摘要

In this paper, a method of constructing C~1 triangular patch using C-curves is presented. C-curves are developed by using the basis {sin t,cos t, t, 1} by Zhang, Pottmann and Wagner, and it overcomes some shortcomings of the non-uniform rational B-splines (NURBS) model. For example, it can represent exactly transcendental curves such as the helix and the cycloid. So, how to develop C-curve into surface becomes a very important problem. In Ref. (3), tensor product quadrilateral patches have been constructed using C-curves. By using the side-vertex method proposed by Nielson, a method for constructing C' triangular patch using C-curves is proposed in this paper. The constructed triangular patch interpolates the positions and the first derivatives of the boundary composite C-Bezier curves.